An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables

@article{Nam2010AnMU,
  title={An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables},
  author={Sung Sik Nam and Hong-Chuan Yang and Mohamed-Slim Alouini and Dong In Kim},
  journal={IEEE Transactions on Information Theory},
  year={2010},
  volume={56},
  pages={5655-5672}
}
Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs). With the proposed approach, we can systematically derive the joint statistics of any partial sums of ordered statistics, in terms of the moment generating function (MGF) and the probability density function (PDF). Our MGF-based approach applies not only when… 

Figures from this paper

Systematic and Unified Stochastic Tool to Determine the Multidimensional Joint Statistics of Arbitrary Partial Products of Ordered Random Variables

A systematic and unified stochastic tool to determine the joint statistics of partial products of ordered random variables (RVs) in terms of the Mellin transform and the probability density function in a unified way is introduced.

New Closed-Form Results on Ordered Statistics of Partial Sums of Gamma Random Variables and Its Application to Performance Evaluation in the Presence of Nakagami Fading

The exact closed-form results on order statistics of any arbitrary partial sums of gamma random variables with the closed- form results of core functions specialized for independent and identically distributed Nakagami- $m$ fading channels based on a moment generating function-based unified analytical framework are presented.

Technical Report: Finger Replacement Schemes for RAKE Receivers in the Soft Handover Region with Multiple BSs over I.N.D. Fading Channels

A general comprehensive framework for the performance assessment of the proposed finger replacement schemes operating over independent and non-identically distributed faded paths is presented.

An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered i.n.d. Random Variables

This paper extends the previous analysis and introduces a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs in the more general case in which the random variables are independent but not necessarily identically distributed.

Joint Statistics of Partial Sums of Ordered Exponential Variates and Performance of GSC RAKE Receivers over Rayleigh Fading Channel

Some new order statistics results are capitalize on to derive exact closed-form expressions for the capture probability and outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels, and compare it to that of partial RAke receivers.

New Statistical Results of Partial Sums of Ordered Gamma-Distributed RVs for Performance Evaluation of Wireless Communication Systems

With the increase in the complexity of communication systems, order statistics have become increasingly significant in performance evaluation, especially for advanced diversity techniques over fading

A robust auto‐adaptive approach for serial acquisition of generalized multi‐carrier spread spectrum in multipath fading mobile channels

In this paper, a new robust auto‐adaptive approach for pseudo‐noise (PN) code acquisition is proposed. It is applied to the generalized multi‐carrier direct‐sequence code‐division multiple‐access (MC

A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

A unified rare-event estimator derived from the well-known multilevel splitting algorithm is proposed for the performance evaluation of wireless communication systems and finds that it compares favorably with existing estimators.

MGF Approach to Compute the Packet Error Probability and Throughput for OFDM, CDMA and MC-CDMA Systems

In this paper, we present a new approach to evaluate the packet error probability (PEP) of code-division multiple access (CDMA), multi-carrier CDMA (MC-CDMA) and orthogonal frequency-division

An Accurate Sample Rejection Estimator for the Estimation of Outage Probability of EGC Receivers

This work was supported by the KAUST Office of Sponsored Research (OSR) under Award No. URF/1/2584-01-01 and the Alexander von Humboldt Foundation.

References

SHOWING 1-10 OF 28 REFERENCES

Analysis of minimum selection H-S/MRC in Rayleigh fading

This work analyzes the error performance of an improved hybrid selection/maximal-ratio combining technique called minimum selection H-S/MRC in flat Rayleigh fading for coherent digital modulation schemes and derives a closed-form expression for the distribution of the number of selected branches.

An Introduction to Probability Theory and Its Applications

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

A statistical model of urban multipath propagation

An urban multipath propagation experiment, involving the simultaneous transmission from a fixed site of 100-ns pulses at 488, 1280, and 2920 MHz and their reception at a mobile van, is described. A

A model for the multipath delay profile of fixed wireless channels

Analysis of the data suggests that, for directive terminal antennas, the delay profile can be modeled as having a "spike-plus-exponential" shape, i.e., a strong return at the lowest delay, plus a set of returns whose mean powers decay exponentially with delay.

Impulse Response Modeling of Indoor Radio Propagation Channels

It is shown that the number of multipath components in each impulse response estimate is a normally-distributed random variable with a mean value that increases with increasing antenna separations, and the RMS delay spread over large areas is normally distributed with mean values that increase with increasing antennas separation.

Systolic architectures for radar CFAR detectors

Radar constant false alarm rate (CFAR) detectors, which are adaptive threshold detectors used to compensate for unknown noise environments, are discussed and systolic array architectures are proposed for several important CFAR detectors.

An MGF-based performance analysis of generalized selection combining over Rayleigh fading channels

Using the notion of the "spacing" between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is

Cooperative Selection Combining in Body Area Networks: Switching Rates in Gamma Fading

It is shown that `everyday' switching rates are slow enough to allow cooperative BAN, and results from BAN measurements approximate three-branch analytical results, and branch approximate independence is validated.